Chaos in a Weakly Nonlinear Oscillator With Parametric and External Resonances

[+] Author and Article Information
K. Yagasaki

Department of Mechanical Engineering, Tamagawa University, Machida, Tokyo 194, Japan

J. Appl. Mech 58(1), 244-250 (Mar 01, 1991) (7 pages) doi:10.1115/1.2897158 History: Received April 17, 1989; Revised March 01, 1990; Online March 31, 2008


This paper describes a study of the chaotic dynamics of a weakly nonlinear single degree-of-freedom system subjected to combined parametric and external excitation. We consider a case of double resonance in which primary resonances, with respect to parametric and external forces, exist simultaneously. By using the averaging method and Melnikov’s technique, it is shown that chaos may occur in certain parameter regions. These chaotic motions result from the existence of orbits homoclinic to a normally hyperbolic invariant torus which corresponds to a hyperbolic periodic orbit in the averaged system. The mechanism and structure of chaos in this situation are also described. Furthermore, the existence of steady-state chaos is demonstrated by numerical simulation.

Copyright © 1991 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In